An emf of $15\, V$ is applied to a circuit containing $5\, H$ inductance and $10\, \Omega$ resistance. The ratio of currents at time $t = \infty$ and $t = 1\, s$ is
According to the question, The circuit as shown below,
The current in the circuit, $I(t) = I(\infty) - [I(\infty) - I(0)]e^{-t/\tau} \dots$(i) $\because$ Time constant, $\tau = \frac{L}{R} = \frac{5}{10} = \frac{1}{2} sec$ at $t \to \infty$, inductor behaves as short circuit hence circuit will be
So, $I(\infty)=\frac{15}{10}=1.5 \,A \dots$(ii) at $t \rightarrow 0$, inductor behaves as open circuit so, no current flow in the circuit, $I(0)=0$ So from E (i), $\Rightarrow I(t) =1.5-(1.5-0) e^{\frac{-t}{(1 / 2)}}=1.5\left(1-e^{-2 t}\right) $ at $ t =1 \,sec , \Rightarrow I(1)=1.5\left(1-e^{-2}\right) \ldots$ (iii) From E (ii) and (iii), we get $\Rightarrow \frac{I(\infty)}{I(1)}=\frac{1.5}{1.5\left(1-e^{-2}\right)}=\frac{e^{2}}{e^{2}-1}$
Inductance is a key parameter in electrical and electronic circuit designs. Like resistance and capacitance, it is a basic electrical measurement that affects all circuits to some degree.
Inductance is used in many areas of electrical and electronic systems and circuits. The electronic components can be in a variety of forms and may be called by a variety of names: coils, inductors, chokes, transformers, . . . Each of these may also have a variety of different variants: with and without cores and the core materials may be of different types.
There are two ways in which inductance is used:
Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect of caused by the current flow. It can be seen that self-inductance applies to a single circuit - in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.
